A group of adults and kids went to see a movie. Tickets cost $$7.50$ each for adults and $$3.50$ each for kids, and the group paid $$43.50$ in total. There were $3$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Explanation: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${7.5x+3.5y = 43.5}$ ${x = y-3}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-3}$ for $x$ in the first equation. ${7.5}{(y-3)}{+ 3.5y = 43.5}$ Simplify and solve for $y$ $ 7.5y-22.5 + 3.5y = 43.5 $ $ 11y-22.5 = 43.5 $ $ 11y = 66 $ $ y = \dfrac{66}{11} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-3}$ to find $x$ ${x = }{(6)}{ - 3}$ ${x = 3}$ You can also plug ${y = 6}$ into ${7.5x+3.5y = 43.5}$ and get the same answer for $x$ ${7.5x + 3.5}{(6)}{= 43.5}$ ${x = 3}$ There were $3$ adults and $6$ kids.